The invention relates to a method for generating an artefact-reduced voxel data record of an object to be examined, with the aid of a computed tomography scanner and to a computer program product in this respect.
X-ray computed tomography (CT) is a method for obtaining information about the interior of objects. Computed tomography originates from the medical field but, in the meantime, it is also used in the industrial field for material analysis and for non-destructive examinations.
In x-ray computed tomography, artefacts arise as a result of various effects, e.g. as a result of the employed reconstruction method and as a result of beam hardening. The examination results can be influenced significantly by metallic artefacts, particularly in the case of industrial computed tomography, i.e. in the examination of technical objects such as e.g. printed circuit boards by way of computed tomography. Thus, metallic artefacts can cause e.g. streaks in the reconstructed data records and/or make the identification of structures which adjoin the metals more difficult or prevent the latter. Reconstruction and beam hardening artefacts also have a negative influence on the quality of x-ray computed tomography data records and can cause problems during further use of the data (e.g. in the case of edge detection algorithms).
Previous methods for reducing artefacts are either very time and computationally intensive or can only correct specific parts of the object to be examined, e.g. non-metallic parts.
It is therefore an object of the present invention to provide a method and a computer program product, by means of which artefacts, in particular reconstruction and beam hardening artefacts, can be reduced in computed tomography.
This object is achieved by the subject matter of the coordinate claims. Advantageous embodiments are the subject matter of the dependent claims.
A first independent aspect for achieving the object relates to a method for generating an artefact-reduced voxel data record of an object to be examined, with the aid of a computed tomography scanner, comprising the following steps in the specified sequence:                generating a first image data record by acquiring a multiplicity of first computed tomography images of the object, wherein an acquisition angle in respect of a first axis of rotation is modified between the acquisition of the first computed tomography images;        tilting the object by a predetermined tilt angle in respect of a second axis of rotation which is arranged substantially orthogonal to the first axis of rotation;        generating a second image data record by acquiring a multiplicity of second computed tomography images of the object tilted about the second axis of rotation;        generating the voxel data record of the object to be examined, with the aid of an iterative image data reconstruction algorithm which uses both the generated first image data record and the generated second image data record as an input data record.        
Within the meaning of this description, a three-dimensional (3D) voxel data record or else volume data record is understood to mean a data record which comprises a multiplicity of voxels. Here, a voxel is a grid point or pixel in a three-dimensional grid or coordinate system. Hence, the multiplicity of voxels of the voxel data record represents the three-dimensional volume of the object to be examined, in the form of discrete points. The voxel data record comprises a value for each voxel, which value describes the attenuation of x-ray radiation at the location of the voxel, i.e. at a specific three-dimensional point of the object to be examined.
The term “acquisition” of images comprises, in particular, recording or measuring images.
A first image data record is generated by acquiring a multiplicity of first computed tomography images, i.e. a first series of images or a first image sequence, of the object. The images are acquired with the aid of an acquisition unit which comprises one or more detectors, e.g. a flat-panel detector. In particular, the first image data record comprises a multiplicity of first computed tomography images or a first series of images or a first image sequence. The individual images of the first image data record are in each case acquired from different perspectives, or acquisition or recording angles. To this end, an acquisition angle is modified in respect of a first axis of rotation of the object or of the computed tomography scanner between the acquisition of the first computed tomography images. By way of example, the object can be rotated about an axis of rotation between the acquisition of the individual images. Alternatively or additionally, an acquisition unit can be rotated about an axis of rotation between the acquisition of the individual images. In particular, each image of the first image data record can be associated with a specific perspective or a specific acquisition angle. Preferably, the first image data record comprises images for acquisition angles from 0° to 180°, more preferably from 0° to 360°.
Accordingly, a second image data record is generated by acquiring a multiplicity of second computed tomography images, i.e. a second series of images or a second image sequence, of the object. The images are acquired with the aid of an acquisition unit which comprises one or more detectors, e.g. a flat-panel detector. In particular, the second image data record comprises a multiplicity of second computed tomography images or a second series of images or a second image sequence. Just like the images of the first image data record, the individual images of the second image data record are in each case acquired from different perspectives, or acquisition or recording angles. To this end, the acquisition angle is modified in respect of the first axis of rotation of the object or of the computed tomography scanner between the acquisition of the second computed tomography images. By way of example, the object can be rotated about an axis of rotation between the acquisition of the individual images. Alternatively or additionally, an acquisition unit can be rotated about an axis of rotation between the acquisition of the individual images. In particular, each image of the second image data record can be associated with a specific perspective or a specific acquisition angle. Preferably, the second image data record comprises images for acquisition angles from 0° to 180°, more preferably from 0° to 360°.
Between the acquisition of the first computed tomography images and the acquisition of the second computed tomography images, the object is tilted by a predetermined or prescribed tilt angle in respect of a second axis of rotation. The second axis of rotation is oriented substantially orthogonal to the first axis of rotation. Preferably, the second axis of rotation corresponds to an optical axis of the computed tomography scanner, wherein the optical axis is defined e.g. by the connecting line between an x-ray source and the detector of the computed tomography scanner. In principle, the tilt angle can assume any value greater than 0° and less than 360°. By way of example, the tilt angle is approximately 30°, 60° or 120°. Preferably, the tilt angle is approximately 90°.
Furthermore, the first and/or second image data record preferably comprises metadata for each acquired image, which metadata describe the position and/or the perspective or the acquisition angle of the object.
Both the first image data record and the second image data record form the input data record for an iterative image data reconstruction algorithm, by means of which the artefact-reduced voxel data record of the object to be examined is generated or calculated.
It is also possible that, in addition to the first image data record and second image data record, one or more further image data records, e.g. a third, fourth, fifth, etc. image data record, is/are generated in a manner analogous to the first image data record and second image data record, wherein the object is tilted in relation to the second axis of rotation, in particular by the predetermined tilt angle or by a different predetermined tilt angle, between the acquisition of the images associated with the respective image data records in each case.
In the method according to the invention, a plurality of x-ray data records are advantageously combined during the reconstruction in order to reduce the artefacts and in order to improve the accuracy of values which are obtained from the voxel data. It was found that artefacts such as reconstruction and beam hardening artefacts generally have a directional dependence and, in particular, extend away from the structures in the voxel data record in a manner orthogonal to the employed axis of rotation.
As a result of two image data records of the object being generated or recorded in the method according to the invention, said image data records differing in that the object is tilted or rotated orthogonally in relation to the first axis of rotation, in particular by 90 degrees, between the recording of the first image data record and of the second image data record, the arising artefacts extend in different directions. The iterative image data reconstruction algorithm simultaneously uses both data records of the same object in different orientations as input and, as a result, supplies a voxel data record with significantly reduced artefacts.
In a preferred embodiment of the method according to the invention, the iterative image data reconstruction algorithm is based on a maximum likelihood expectation maximization (MLEM) algorithm.
In particular, the iterative image data reconstruction algorithm is a modified MLEM algorithm which is designed to use or process a plurality of different image data records, in particular two image data records, of the object simultaneously as an input or as an input data record. An artefact-reduced voxel data record can be calculated iteratively on the basis of the two image data records or on the basis of the plurality of image data records by means of the modified MLEM algorithm.
In a further preferred embodiment of the method according to the invention, the image data reconstruction algorithm comprises a calculation of a normalization volume data record, wherein the normalization volume data record emerges as a sum of a normalization volume data record associated with the first image data record and a normalization volume data record associated with the second image data record.
Expressed in formulae, the normalization volume data record norm is calculated as follows:norm=Prot1T(normseq1)+Prot2T(normseq2)  (1),whereProtT(I) generally represents a transposed projection or a back projection of an image sequence I, which is rotated by the inverted quaternion rot. The index 1 in Equation (1) in this case means that the back projection relates to first image data record, while the index 2 accordingly means that the back projection relates to the second image data record. In particular, rot1 is a quaternion which describes the rotation of the object for the first image data record, with rot1 therefore being an identical rotation, i.e. rot1:=1. Accordingly, rot2 is a quaternion which describes the rotation of the object for the second image data record. To the extent that the tilt of the object between the acquisition of the images of the first image data record and the acquisition of the images of the second image data record is 90° about the z-axis, the following applies:
      rot    ⁢                  ⁢    2    =            1              2              +          k      ⁢                        1                      2                          .            normseq1 means a normalized image sequence of the first image data record and normseq2 means a normalized image sequence of the second image data record.In particular,normseq1:=1 and normseq2:=1  (2)are set in Equation (1).
In a further preferred embodiment of the method according to the invention, the image data reconstruction algorithm comprises a calculation of a projection associated with the first image data record and a projection associated with the second image data record. In particular, the calculation of the projection associated with the second image data record comprises a coordinate transform on the basis of the orientation of the tilted object.
Expressed in formulae, a projectionproj1:=Prot1(voln)  (3)belonging to the first image data record and a projectionproj2:=Prot2(voln)  (4)belonging to the second image data record are calculated. Here, voln means the volume data record in the nth iteration step.
In a further preferred embodiment of the method according to the invention, each pixel of the generated first image data record is divided by the corresponding pixel of the projection associated with the first image data record, as result of which a modulated projection
      proj    1    *    :=            input      1              proj      1      associated with the first image data record is obtained. Furthermore, each pixel of the generated second image data record is divided by a corresponding pixel of the projection associated with the second image data record, as a result of which a modulated projection
      proj    2    *    :=            input      2              proj      2      associated with the second image data record is obtained.
In a further preferred embodiment of the method according to the invention, a back projection, preferably an unfiltered back projection, is calculated on the basis of the modulated projection proj1* associated with the first image data record and the modulated projection proj2* associated with the second image data record.
In a further preferred embodiment of the method according to the invention, the back projection is calculated as a sum of a back projection, preferably an unfiltered back projection, associated with the first image data record and a back projection, preferably an unfiltered back projection, associated with the second image data record.
Expressed in formulae, this back projection is calculated as follows:backproj:=Prot1T(proj1*)+Prot2(proj2*)  (5).
A further independent or alternative aspect for achieving the object relates to a method for generating an artefact-reduced 3D voxel data record of an object to be examined, with the aid of a computed tomography scanner, comprising the following steps in the specified sequence:                generating a first image data record by acquiring a multiplicity of first computed tomography images of the object, wherein an acquisition angle in respect of a first axis of rotation is modified between the acquisition of the first computed tomography images;        tilting the object by a predetermined tilt angle in respect of a second axis of rotation which is arranged substantially orthogonal to the first axis of rotation;        generating a second image data record by acquiring a multiplicity of second computed tomography images of the object tilted about the second axis of rotation;        reconstructing the first image data record in a first coordinate system;        generating a second coordinate system by rotating the first coordinate system on the basis of the orientation of the tilted object;        reconstructing the second image data record in the second coordinate system;        generating the voxel data record of the object to be examined, by data fusion of the reconstructed image data records.        
The explanations made above or below in respect of the embodiments of the first aspect also apply to the aforementioned further independent or alternative aspect and, in particular, to embodiments preferred in this respect. In particular, the explanations made above and below in respect of the embodiments of the respective other aspects in particular also apply to an independent aspect of the present invention and to embodiments preferred in this respect.
In accordance with the alternative aspect of the present invention, the reconstruction of the first image data record and of the second image data record respectively is carried out in a first coordinate system and a second coordinate system. Here, the second coordinate system emerges from the first coordinate system by rotating the first coordinate system on the basis of the orientation of the tilted object. In particular, the second coordinate system emerges by rotating the first coordinate system about the predetermined tilt angle. Thus, the rotation is carried out, in particular, in such a way that the orientation of the reconstructed object is substantially identical in respect of the first coordinate system and of the second coordinate system.
Within the meaning of this description, “data fusion” is understood to mean a combination of data, with the data fusion in particular comprising an evaluation.
Two reconstructed image data records, i.e. two resultant voxel data records or volumes, are inherently aligned by means of the method according to the invention. This makes the step of the data fusion easier since no adaptation of the image data records in respect of the object orientation is required anymore during the data fusion. The only difference between the values of the mutually corresponding voxels in the two resultant volumes is either noise or an artefact. As a result of a second coordinate system being generated by rotating the first coordinate system prior to the reconstruction of the second image data record according to the invention, wherein the second image data record is reconstructed in said second coordinate system, the method according to the invention is only accompanied by a single interpolation step. Since each interpolation step is time intensive in view of the voxel data record and, moreover, may be afflicted by errors, the method according to the invention is superior in terms of speed and quality over conventional methods, in which two or more interpolation steps are required.
In a preferred embodiment of the method according to the invention, the second coordinate system is obtained or calculated from the first coordinate system by means of the following transformation:G2(0,x2,y2,z2)=rot2×G1(0,x2,y2,z2)×rot2*  (6).
Here G1 denotes the first coordinate system, G2 denotes the second coordinate system, rot2 denotes a rotation quaternion and rot2* denotes the rotation quaternion conjugate to rot2.
The use of quaternions is simpler in handling compared to Eulerian angles and advantageously avoids the possibility of a gimbal lock.
In a further preferred embodiment of the method according to the invention, the reconstruction of the first image data record and/or the second image data record is based on a back projection, preferably a filtered back projection. In particular, the reconstruction of the first image data record and/or the second image data record is carried out by means of a modified back projection, preferably a filtered back projection.
However, in principle, it is also possible for the reconstruction alternatively to be based on an MLEM or for it to be carried out by means of an MLEM.
In a further preferred embodiment of the method according to the invention, the modified back projection comprises a rotation of voxel coordinates (x,y,z):(0,x′,y′,z′):=rot*·(ix+jy+kz)·rot  (7),where (x′,y′,z′) denote coordinates of the rotated coordinate system. The multiplications are quaternion multiplications in each case and rot* is the conjugate quaternion of rot.
In a further preferred embodiment of the method according to the invention, the data fusion of the reconstructed image data records comprises an extremal value formation, i.e. a formation of a minimum or a formation of a maximum, of mutually corresponding voxels of the first reconstructed image data record and the second reconstructed image data record.
In other words, the smallest or largest intensity value of the two mutually corresponding voxels of the first reconstructed image data record and the second reconstructed image data record is used for the resultant or fused voxel data record:volƒ(x,y,z)=min{vol1(x,y,z),vol2(x,y,z)}  (8a),orvolƒ(x,y,z)=max{vol1(x,y,z),vol2(x,y,z)}  (8b).
In general terms, the data fusion can be carried out by means of a function ƒ in a manner dependent on the reconstructed first image data record and the reconstructed second image data record:volƒ(x,y,z)=ƒ{vol1(x,y,z),vol2(x,y,z)}  (8c).
In addition to forming the minimum and forming the maximum, this function can also comprise other calculation operations, such as e.g. forming an average value. However, within the scope of the present invention, the extremal value formation, i.e. the formation of a minimum or a maximum, was surprisingly found to be particularly effective.
A further independent aspect for achieving the object relates to a computer program product which comprises machine-readable program code which, when loaded onto a computer, is suitable for executing the method according to the invention.
Below, individual embodiments for achieving the object are described in an exemplary manner on the basis of the figures. Here, the individual described embodiments in part have features which are not mandatory for carrying out the claimed subject matter, but which provide desired properties in specific cases of application. Thus, embodiments which do not have all features of the embodiments described below should be considered to be disclosed as falling under the described technical teaching. Furthermore, certain features are only mentioned in relation to individual embodiments described below in order to avoid unnecessary repetition. Therefore, reference is made to the fact that the individual embodiments should be considered not only on their own, but also in an overview. On the basis of this overview, a person skilled in the art will identify that individual embodiments can also be modified by including individual features or a plurality of features from other embodiments. Reference is made to the fact that a systematic combination of the individual embodiments with individual features or with a plurality of features, which are described in relation to other embodiments, may be desirable and expedient, and should therefore be contemplated and also be considered to be comprised by the description.